Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media

2021 ◽  
Author(s):  
Nicolae Suciu ◽  
Davide Illiano ◽  
Alexander Prechtel ◽  
Florin Radu
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Random Walk ◽  
Transport Processes ◽  
Richards Equation ◽  
Unsaturated Porous Media ◽  
Coupled Flow ◽  
Flow And Transport ◽  
Coupled Flow And Transport ◽  
Fully Coupled

<p>We present new random walk methods to solve flow and transport problems in saturated/unsaturated porous media, including coupled flow and transport processes in soils, heterogeneous systems modeled through random hydraulic conductivity and recharge fields, processes at the field and regional scales. The numerical schemes are based on global random walk algorithms (GRW) which approximate the solution by moving large numbers of computational particles on regular lattices according to specific random walk rules. To cope with the nonlinearity and the degeneracy of the Richards equation and of the coupled system, we implemented the GRW algorithms by employing linearization techniques similar to the <em>L</em>-scheme developed in finite element/volume approaches. The resulting GRW <em>L</em>-schemes converge with the number of iterations and provide numerical solutions that are first-order accurate in time and second-order in space. A remarkable property of the flow and transport GRW solutions is that they are practically free of numerical diffusion. The GRW solvers are validated by comparisons with mixed finite element and finite volume solvers in one- and two-dimensional benchmark problems. They include Richards' equation fully coupled with the advection-diffusion-reaction equation and capture the transition from unsaturated to saturated flow regimes.  For completeness, we also consider decoupled flow and transport model problems for saturated aquifers.</p>

Vadose Zone, Part I : Characterization and Flow Processes

2003 ◽  
Author(s):  
Yoram Rubin
Keyword(s):  
Porous Media ◽  
Water Flow ◽  
Governing Equation ◽  
Vadose Zone ◽  
Stochastic Analysis ◽  
Transport Processes ◽  
Richards Equation ◽  
Saturated Porous Media ◽  
Flow And Transport ◽  
Flow Processes

Many of the principles guiding stochastic analysis of flow and transport processes in the vadose zone are those which we also employ in the saturated zone, and which we have explored in earlier chapters. However, there are important considerations and simplifications to be made, given the nature of the flow and of the governing equations, which we explore here and in chapter 12. The governing equation for water flow in variably saturated porous media at the smallest scale where Darcy’s law is applicable (i.e., no need for upscaling of parameters) is Richards’ equation (cf. Yeh, 1998)

Compatible Numerical Schemes for Coupled Flow and Transport in Porous Media

2006 ◽  
Author(s):  
Azad Q. Zade ◽  
Mehrdad T. Manzari ◽  
Siamak K. Hannani
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Mixed Finite Element ◽  
Mass Conservation ◽  
Numerical Schemes ◽  
Local Conservation ◽  
Coupled Flow ◽  
Flow Equations ◽  
Flow And Transport ◽  
Solution Algorithms

In this paper, the compatibility of various combinations of numerical schemes for the solution of flow and transport equations in porous media is studied and the possible loss of accuracy and global mass conservation are investigated. Here, the flow equations are solved using three popular finite element methods including the Standard Galerkin (SG), Discontinuous Galerkin (DG) and Mixed Finite Element (MFE) methods among which only the DG method possesses the local conservation property. Besides, the transport of a scalar variable which is governed by a convection-diffusion equation is studied in conjunction with the flow equations. The transport equation is solved using both the Streamline Upwind Petrov-Galerkin (SUPG) and the DG methods. Two test cases are numerically solved using various combinations of methods in order to explore the compatibility of flow and transport solution algorithms. In each test case, the error in total mass conservation and the deviation from the exact solution are compared for various solver combinations.

scholarly journals Modeling Flow and Transport in Unsaturated Porous Media: A Review

2000 ◽  
Vol 5 ◽  
pp. 265
Author(s):  
H.H. Al-Barwani ◽  
M. Al-Lawatia ◽  
E. Balakrishnan ◽  
A. Purnama
Keyword(s):  
Porous Media ◽  
Contaminant Transport ◽  
Water Flow ◽  
Unsaturated Zone ◽  
Unsaturated Flow ◽  
Numerical Solutions ◽  
Transport Processes ◽  
Field Conditions ◽  
Unsaturated Porous Media ◽  
Flow And Transport

Underground water is a vital natural resource and every effort should be made to understand ways and means of efficiently using and managing it. The unsaturated zone, bounded at its top by the land surface and below by the water table, is the region through which water, together with pollutant carried by the water, infiltrates to reach the groundwater. Therefore, various processes occurring within the unsaturated zone play a major role in determining both the quality and quantity of water recharging into the groundwater. Classical methods of predicting water flow and contaminant transport processes in unsaturated porous media are generally inadequate when applied to natural soils under field conditions, due to the occurrence of macropores, structured elements and spatial variability of soil properties. Contaminant transport models also require the simultaneous solution of the unsaturated flow and transport equations. For applications to field conditions, numerical solutions and computer simulations based on numerical models have been increasingly used. Advances and progress in modeling water flow and contaminant transport in the unsaturated zones are reviewed, and specific research areas in need of future investigation especially relevant to Oman are outlined.

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